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wherever turn your helm -> should be "turns" (singular) but I can't say the expression sounds familiar.
"helm" is also a helmet. Together with the "shield", that makes me think of a knight turning his head around.

ask [...] where a misty fog and haze -> you need a verb here.
"where are" at the very least...

That is obviously a proper correction. Although today I found some interesting deviation from the norms on English language, namely the use of "IS" verb fro two uncountable nouns:
There is thunder and lightning in the sky.
The thunder and lightning is pretty scary, huh?
You could follow this grammarians' talk over there: https://ell.stackexchange.com/questions/9968/verb-for-two-uncountable-items

articles: "Dew" is uncountable, "field" is countable. (and dew can't "fall" imho)
I hope my prayer would be you shield wherever turns your helm. > I did't get the meaning of this one at all. There is probably a typo [your?] as well as a missing subject.
where a misty fog and haze: > a verb is missing (as silenced mentioned)
what shelter fate for you prepares and where would lead your ways. > same as above ^: a verb is missing and a subject is missing
Вы — в дыме поезда... — > "The train among the sad fields slips",
What did happen to the train exactly? Someone could slip on the banana coat, but it doesn't pair well with the train.
Поля В вечерней жалобе > the smoke blows on your neck. [ i would suggest a different translation there]

I guess "helm" is meant as a ship's steering wheel (as in "whichever way you go"), but you would rather "turn the helm" to steer a ship than having it turn by itself, and the other meaning of the word (a heavy helmet) makes the sentence quite confusing.

I know this expression, I didn't realize that the "helm" is a subject there.
Imho, someone could be "at the helm" (and do the steering) but not the other way around.
Check out the link I posted above, it is pretty interesting (at least to me)

Treating compound nouns like "Sturm und Drang" as single entities is a possibility in French too, so that sounds rather natural to me.
We also have countable and uncountable objects, though the "always singular" ones like "sheep" or "hair" are far less common than in English.

what's shelter -> this time you have a verb too many
"what shelter" is the object complement there

a mast of a big ship -> *the* mast of *a* ship (the ship is undefined, but there is only one specific mast on it)

you is on the deck -> you *are*, but I'd rather say "you stand"
"to be" sounds very generic. That's what we would use in French, but English likes to be more specific

I see a strip -> I don't really see what "strip" would mean here. Sounds like some landscape feature, maybe some field, but nothing like the train smoke or the rails.

near the stack -> as "chimney" I guess? Again I would rather use "stand" or whatever specific verb.
The image sounds a bit strange though.
He would have to climb atop the locomotive to stand next to the funnel!

And dew enshrouds the evening fields -> very nice!

the crows fly up and hover -> "fly up" has a very specific meaning. Otherwise I guess it would just mean "'fly in an upwards direction" like left or right.
I suggest "take flight" or maybe "soar up" (that would evoke a billowing cloud of smoke).

four winds let be your cover -> you simply can't violate word ordering here. That changes the meaning, as if you were asking the four winds to give their cover a break
"let the four winds be your cover" is what I would expect. If you omit the article, it sounds like you would pick four winds at random, while *the* four winds is another name for the four cardinal points.
Trouble is, "cover" rather means a fake identity, like a spy working undercover.

Well, except for the unusual word ordering, I think the sentence is syntactically correct now that the " 's " has been removed.
The comma on the first line is rather misleading though.
"a mirror where a haze forever sleeps" is the indirect complement, and the last two lines are the object complement. However, "where" could introduce yet another direct complement (as if asking 3 different things to the mirror instead of 2 things to the-mirror-inside-which-a-haze-sleeps-forever )
"my mirror in which..." would be a lot more explicit.

Since you must use some kind of determinant in English (contrary to Russian), you might as well pick the one that makes the most sense. Both "a" and "my" are the same length, so you are free to choose, while being specific in Russian would add three syllables to the sentence (у своего зеркала).
"a mirror" would feel like she picked a mirror at random, while she most likely would use her own. Hence "my mirror".

On the contrary, you're doing me a favour. I just love chatting about translations.

I agree you can interpret "зеркало" that way, but then I would rather use "some mirror" (i.e. one particular magic mirror, not just the first mirror she can find). It seems to me, "a" is a very generic determinant, like "any" or "whatever".
Still English is not my native language, so I might be wrong.

Ravens soar and whirl -> sounds quite good to me (except "ravens" does not need a capital "R")

for all sides of the world -> "side" does not work well with "the world".
You would rather say "to the four corners of the world" to mean "anywhere you might go".
Except it's too long
"Everywhere/anywhere in the world" would be the proper length, but a bit bland maybe.

You mean a crow cannot hover like, say, a hummingbird?
Still you can use the term to describe the birds staying airborne within a limited area, or can't you?
I know this is far from foolproof, but Google offers a rich choice of use cases.